What do you think of Max Tegmark’s answer, that it’s because universes with every possible (i.e., non-contradictory) set of laws of physics exist and we happen to be in one with electromagnetic dynamics derived from Maxwell’s Lagrangian?
I think Tegmark’s idea is either tautological or preposterous, depending on what he means by exist. If exist means ‘exist in an abstract, mathematical sense’ (as it does in the sentence There exist infinitely many prime numbers) then it’s tautological, and if it means ‘physically exist in this particular universe (i.e., the set of everything that can interact or have interacted with us, or interact or have interacted with something that can interact or have interacted with us, etc.)’ (as it does in the sentence Santa does not exist), it’s preposterous. The last chapter in Good and Real by Gary Drescher elaborates on this.
Once again, we badly need different words for ‘be mathematically possible’ and ‘be part of this universe’.
I assume he means they exist in the same sense as observers can only find themselves in places that exist. Which does not require any possibility of interaction between any two things that happen to exist.
I think Tegmark’s idea is either tautological or preposterous, depending on what he means by exist.
From what I can tell, Tegmark doesn’t mean either of the options you provide. It is closer to the first option (‘exist in the abstract’) but without all the implied privilege for the universe that happens to have you in it. The difference seems significant.
I don’t know too much about Tegmark, but I’m pretty sure he doesn’t have your second meaning in mind.
That said, I’m not sure your first meaning is actually tautological, given that for Tegmark’s idea to be an answer as Wei_Dai suggests, whatever “exist” means it has to encompass the kind of thing that you are doing right now.
The idea that things which “exist in an abstract mathematical sense” can, solely by virtue of that, do what you’re doing right now is perhaps tautological, but if so the tautology is not one that most humans will readily recognize as one.
Yes, I was unintentionally implicitly assuming that this universe is a mathematical structure. (OTOH, ISTM that this is a somewhat standard assumption on LW, e.g. Solomonoff induction wouldn’t make that much sense without it.)
Escape the first underscore by putting a backslash before it. (Why does the MarkDown italics mark-up work even within words, anyway? I think the situations where someone would want to italicize only part of a word are far fewer than those where one would want to use a word with an underscore in the middle of it.)
Why does the MarkDown italics mark-up work even within words, anyway? I think the situations where someone would want to italicize only part of a word are far fewer than those where one would want to use a word with an underscore in the middle of it.
I would think a lot less of a language that introduced an arbitrary limitation on its syntax like that. Italics of parts of a word come up occasionally and bold letters of a word more frequently than that. The language arbitrarily deciding it doesn’t want to execute the formatting commands unless you do whole words the same would be irritating, confusing and inelegant.
And it makes the rare-but-still-occasionally-desired case doable without escaping into HTML (which is not possible in LW’s no-HTML subset of Markdown).
You’d only need, whenever you see an underscore, to check whether the previous character is whitespace (or punctuation, e.g. a left parenthesis). Arundelo’s point seems more valid to me (though you might allow to escape spaces, e.g. _n_\ th… but that’d be more complicated).
I think Tegmark’s idea is either tautological or preposterous, depending on what he means by exist. If exist means ‘exist in an abstract, mathematical sense’ (as it does in the sentence There exist infinitely many prime numbers) then it’s tautological, and if it means ‘physically exist in this particular universe (i.e., the set of everything that can interact or have interacted with us, or interact or have interacted with something that can interact or have interacted with us, etc.)’ (as it does in the sentence Santa does not exist), it’s preposterous. The last chapter in Good and Real by Gary Drescher elaborates on this.
Once again, we badly need different words for ‘be mathematically possible’ and ‘be part of this universe’.
I assume he means they exist in the same sense as observers can only find themselves in places that exist. Which does not require any possibility of interaction between any two things that happen to exist.
From what I can tell, Tegmark doesn’t mean either of the options you provide. It is closer to the first option (‘exist in the abstract’) but without all the implied privilege for the universe that happens to have you in it. The difference seems significant.
I don’t know too much about Tegmark, but I’m pretty sure he doesn’t have your second meaning in mind.
That said, I’m not sure your first meaning is actually tautological, given that for Tegmark’s idea to be an answer as Wei_Dai suggests, whatever “exist” means it has to encompass the kind of thing that you are doing right now.
The idea that things which “exist in an abstract mathematical sense” can, solely by virtue of that, do what you’re doing right now is perhaps tautological, but if so the tautology is not one that most humans will readily recognize as one.
Yes, I was unintentionally implicitly assuming that this universe is a mathematical structure. (OTOH, ISTM that this is a somewhat standard assumption on LW, e.g. Solomonoff induction wouldn’t make that much sense without it.)
Perhaps. But the connotations of saying that something exists in an abstract, mathematical sense tend to run counter to that.
Escape the first underscore by putting a backslash before it. (Why does the MarkDown italics mark-up work even within words, anyway? I think the situations where someone would want to italicize only part of a word are far fewer than those where one would want to use a word with an underscore in the middle of it.)
I would think a lot less of a language that introduced an arbitrary limitation on its syntax like that. Italics of parts of a word come up occasionally and bold letters of a word more frequently than that. The language arbitrarily deciding it doesn’t want to execute the formatting commands unless you do whole words the same would be irritating, confusing and inelegant.
It’s probably less work to read character-by-character than to split on words and read the first and last character of each.
And it makes the rare-but-still-occasionally-desired case doable without escaping into HTML (which is not possible in LW’s no-HTML subset of Markdown).
You’d only need, whenever you see an underscore, to check whether the previous character is whitespace (or punctuation, e.g. a left parenthesis). Arundelo’s point seems more valid to me (though you might allow to escape spaces, e.g.
_n_\ th… but that’d be more complicated).True! I do not know why MarkDown italics works within words.